Trig questions. Which ones are true.

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The discussion revolves around verifying the truth of several trigonometric identities. The consensus is that statements a) and b) are false, while c) and d) are true, though d) is questioned for its validity under certain conditions. Participants suggest using a graphing calculator to confirm the equality of the equations in b) and emphasize understanding the underlying concepts rather than just plugging in values. The conversation highlights the importance of verifying trigonometric identities and understanding their implications.
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Which of the following are true?

a) sin (theta − [pi/2]) = sin (theta)
b) (sin [pi/3])(cos [pi/8]) = (sin [(3pi)/8])(cos [(3pi)/8])
c) sin (theta + theta) = sin (2theta)
d) (sin [2theta])/(sin [3theta]) = 2/3

a) F
b) F
c) T
d) T

Tell me I got the right answers, please.
 
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d is wrong. b looks right, but I would want to check it, just to be safe. The others are right.
 


If you have a graphing calculator you can graph both equation to verify they are equal.
 


a: pi/2 is just the phase shift. Will pi/2 make them out of phase?

b: with no variable (Theta) plug and chug in the calculator unless you teacher wants you to prove?

c: does does x+x=2x?

d: when Theta =? or maybe I should say will it for any Theta.
 

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